Is your hermit crab dead if it falls out its shell when you pick up the and move or is molting?

It is likely molting.

When hermit crabs molt, they shed their entire exoskeleton in one piece. This includes their shell, which they normally cannot leave at will. The process can take several days, and the crab will be very vulnerable to predators and injury at this time.

As the crab molts, its exoskeleton breaks at the back behind the eyes. As it molts, it will pull forward, then back, until it is pulled up over the claws and then off the crab entirely. The hermit crab will then eat its own old shell to reclaim the calcium and other minerals within.

However, if the crab is limp or unresponsive, it is likely dead.